One of the most important Italian and European mathematicians of the 19th century, he studied at the Normal School of Higher Studies in Pisa, his native city, under the guidance of Enrico Betti (1823-1892) and Ottaviano Fabrizio Mossotti (1791-1863). Graduating in 1864, he was awarded a scholarship for Paris, where he had the chance to study with Charles Hermite (1822-1901) and Joseph Louis François Bertrand (1822-1900). Appointed Professor of Geodesy at the University of Pisa in 1866, he first concentrated on differential geometry and then, in the following years, on pure analysis. Particularly significant were the results he achieved in the study of series and in the integration of the functions of complex variables. In 1871 he succeeded Betti as full professor in the Chair of Upper Analysis and Geometry of the University of Pisa, beginning at the same time to participate actively in Italian political life and becoming, within a few years' time, first Member of Parliament (1880) and later Senator of the Kingdom (1892). Fundamental for the development of modern mathematics remains his treatise Fondamenti per la teoria delle funzioni di variabili reali [Bases for the theory of functions of real variables] (1878). He is buried in the Monumental Cemetery of Pisa.